Compute the two-top-quark-loop virtual NNLO contributions

Determine the genuine three-loop virtual NNLO contributions to Standard Model Higgs boson pair production via gluon fusion that contain two closed top-quark loops, including the class of diagrams with massless t-channel cuts or an external Higgs boson.

Background

The report explains that a complete NNLO prediction retaining finite top-quark-mass effects requires three-loop virtual amplitudes. Several classes of these amplitudes have been partially computed through expansions in transverse momentum, the Higgs-boson mass, or Mandelstam variables. The class involving two closed top-quark loops is technically more difficult because of massless t-channel cuts and configurations involving an external Higgs boson.

These contributions are necessary for replacing approximate NNLO treatments with a calculation that consistently retains the full top-quark-mass dependence in the virtual sector.

References

The class of diagrams represented in Fig.~\ref{fig::gghh_FDs}(d), which involves two top quark loops, faces the additional challenge of massless cuts in the $t$-channel or isolating an external Higgs boson and therefore requires a more involved asymptotic expansion. They are not yet known, but remain work in progress.

— Higgs Boson Pair Production via Gluon Fusion: Higher-Order Corrections and Theoretical Uncertainties  (2609.04868 - H et al., 4 Sep 2026) in Section 2, subsection “Towards NNLO with full top quark mass dependence”